Mathematics
ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°; calculate :
(i) ∠DAB,
(ii) ∠BDC.
Circles
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Answer
(i) We know that,
Angles in same segment are equal.
∴ ∠DAB = ∠BED = 65°.
Hence, ∠DAB = 65°.
(ii) We know that,
Angle in semi-circle is a right angle.
∴ ∠ADB = 90°.
In △ADB,
⇒ ∠ABD + ∠ADB + ∠DAB = 180°
⇒ ∠ABD + 90° + 65° = 180°
⇒ 155° + ∠ABD = 180°
⇒ ∠ABD = 180° - 155° = 25°.
As, AB || DC
∠BDC = ∠ABD = 25°.
Hence, ∠BDC = 25°.
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